Simulation Study Results

Conditions

Survival Conditions

Setting Regimen Characteristics
1 2 suboptimal, relapse rate is twice that of the control regimen
3,4 minimal, relapse rate is the same as the control regimen
5 desirable, relapse rate is half that of the control regimen
2 2-5 all are desirable, relapse rate is half that of the control regimen
3 2-5 all are minimal, relapse rate is the same as the control regimen

log10(TTP) conditions

  • For each treatment arm, we will do a handful of hypothetical intervention effect sizes. These will be specified as percent change in slope as compared to the control.
    • \(\{10\%,20\%,30\%,40\%\}\) (even relative increases by treatment arm)
    • \(\{-10\%,10\%,35\%,40\%\}\) (two are near the control arm, two are better. Can we distinguish the best?)
    • \(\{35\%, 37\%, 39\%, 41\%\}\)

Visualization of conditions

Simulation Results

Log10(TTP) Only

For the sake of this simulation study, we will consider dropping regimens that fail to meet the following criteria:

  1. \(\pi(\mu_k > \mu) \geq \alpha_1\). The probability that the slope for regimen \(k\) is greater than the control slope must be at least \(\alpha_1 = \{0.8, 0.9, 0.95\}\)
30 per regimen
30 per regimen
P(Continues based off of log10(TTP))
Log10(TTP) Characteristics P(better than control) > 0.8 and P(in top 2) > 0.8 P(better than control) > 0.8 P(better than control) > 0.9 P(better than control) > 0.95
Slopes are evenly distributed
ref 0.00 0.00 0.00 0.00
10% 0.00 0.64 0.47 0.35
20% 0.03 0.94 0.88 0.77
30% 0.59 1.00 0.99 0.96
40% 0.93 1.00 1.00 1.00
Slopes are clustered high
ref 0.00 0.00 0.00 0.00
35% 0.08 1.00 1.00 0.99
37% 0.15 1.00 1.00 1.00
39% 0.22 1.00 1.00 1.00
41% 0.36 1.00 1.00 1.00
Slopes are clustered high and low
ref 0.00 0.00 0.00 0.00
-10% 0.00 0.01 0.01 0.00
10% 0.00 0.64 0.48 0.33
35% 0.97 1.00 1.00 0.99
40% 0.99 1.00 1.00 1.00
40 per regimen
40 per regimen
P(Continues based off of log10(TTP))
Log10(TTP) Characteristics P(better than control) > 0.8 and P(in top 2) > 0.8 P(better than control) > 0.8 P(better than control) > 0.9 P(better than control) > 0.95
Slopes are evenly distributed
ref 0.00 0.00 0.00 0.00
10% 0.00 0.67 0.51 0.37
20% 0.02 0.96 0.90 0.84
30% 0.66 1.00 1.00 0.99
40% 0.98 1.00 1.00 1.00
Slopes are clustered high
ref 0.00 0.00 0.00 0.00
35% 0.08 1.00 1.00 1.00
37% 0.11 1.00 1.00 1.00
39% 0.24 1.00 1.00 1.00
41% 0.40 1.00 1.00 1.00
Slopes are clustered high and low
ref 0.00 0.00 0.00 0.00
-10% 0.00 0.02 0.00 0.00
10% 0.00 0.67 0.50 0.38
35% 0.99 1.00 1.00 1.00
40% 1.00 1.00 1.00 1.00
60 per regimen
60 per regimen
P(Continues based off of log10(TTP))
Log10(TTP) Characteristics P(better than control) > 0.8 and P(in top 2) > 0.8 P(better than control) > 0.8 P(better than control) > 0.9 P(better than control) > 0.95
Slopes are evenly distributed
ref 0.00 0.00 0.00 0.00
10% 0.00 0.78 0.66 0.52
20% 0.00 1.00 0.98 0.95
60% 0.73 1.00 1.00 1.00
40% 1.00 1.00 1.00 1.00
Slopes are clustered high
ref 0.00 0.00 0.00 0.00
35% 0.04 1.00 1.00 1.00
37% 0.18 1.00 1.00 1.00
39% 0.24 1.00 1.00 1.00
41% 0.45 1.00 1.00 1.00
Slopes are clustered high and low
ref 0.00 0.00 0.00 0.00
-10% 0.00 0.00 0.00 0.00
10% 0.00 0.80 0.70 0.53
35% 1.00 1.00 1.00 1.00
40% 1.00 1.00 1.00 1.00
80 per regimen
80 per regimen
P(Continues based off of log10(TTP))
Log10(TTP) Characteristics P(better than control) > 0.8 and P(in top 2) > 0.8 P(better than control) > 0.8 P(better than control) > 0.9 P(better than control) > 0.95
Slopes are evenly distributed
ref 0.00 0.00 0.00 0.00
10% 0.00 0.82 0.72 0.59
20% 0.01 1.00 1.00 1.00
30% 0.87 1.00 1.00 1.00
40% 1.00 1.00 1.00 1.00
Slopes are clustered high
ref 0.00 0.00 0.00 0.00
35% 0.03 1.00 1.00 1.00
37% 0.09 1.00 1.00 1.00
39% 0.26 1.00 1.00 1.00
41% 0.47 1.00 1.00 1.00
Slopes are clustered high and low
ref 0.00 0.00 0.00 0.00
-10% 0.00 0.00 0.00 0.00
10% 0.00 0.86 0.77 0.60
35% 1.00 1.00 1.00 1.00
40% 1.00 1.00 1.00 1.00
Figures

Relapse Only

Tables
Mixed survival conditions
P(stopped for futility on the basis of relapse)
nk regimen At least 1 At least 2 At least 3
Control regimen (relapse rate = 5%)
30 1 0.00 0.00 0.00
40 1 0.00 0.00 0.00
60 1 0.01 0.00 0.00
80 1 0.00 0.00 0.00
Sub-optimal regimen (relapse rate = 10%)
30 2 0.58 0.22 0.05
40 2 0.84 0.53 0.25
60 2 0.95 0.80 0.57
80 2 0.99 0.96 0.88
Minimal regimen (relapse rate = 5%)
30 3 0.38 0.08 0.01
40 3 0.58 0.20 0.05
60 3 0.79 0.47 0.21
80 3 0.90 0.67 0.42
30 4 0.36 0.08 0.01
40 4 0.54 0.18 0.04
60 4 0.77 0.43 0.19
80 4 0.91 0.68 0.43
Desirable regimen (relapse rate = 2.5%)
30 5 0.25 0.03 0.00
40 5 0.35 0.07 0.01
60 5 0.52 0.16 0.03
80 5 0.71 0.34 0.13
P(stopped for futility on the basis of relapse)
nk regimen At least 1 At least 2 At least 3
Control regimen (relapse rate = 10%)
30 1 0.00 0.00 0.00
40 1 0.00 0.00 0.00
60 1 0.01 0.00 0.00
80 1 0.01 0.00 0.00
Sub-optimal regimen (relapse rate = 20%)
30 2 0.84 0.55 0.26
40 2 0.98 0.88 0.70
60 2 1.00 0.99 0.95
80 2 1.00 1.00 1.00
Minimal regimen (relapse rate = 10%)
30 3 0.63 0.27 0.08
40 3 0.83 0.52 0.24
60 3 0.97 0.83 0.62
80 3 0.99 0.95 0.85
30 4 0.62 0.25 0.07
40 4 0.81 0.47 0.21
60 4 0.95 0.81 0.58
80 4 0.99 0.96 0.86
Desirable regimen (relapse rate = 5%)
30 5 0.45 0.11 0.01
40 5 0.57 0.23 0.05
60 5 0.77 0.43 0.18
80 5 0.92 0.71 0.44
P(stopped for futility on the basis of relapse)
nk regimen At least 1 At least 2 At least 3
Control regimen (relapse rate = 3%)
30 1 0.00 0.00 0.00
40 1 0.00 0.00 0.00
60 1 0.00 0.00 0.00
80 1 0.00 0.00 0.00
Sub-optimal regimen (relapse rate = 6%)
30 2 0.39 0.08 0.01
40 2 0.65 0.28 0.08
60 2 0.83 0.52 0.25
80 2 0.95 0.80 0.56
Minimal regimen (relapse rate = 3%)
30 3 0.26 0.03 0.00
40 3 0.40 0.09 0.01
60 3 0.61 0.24 0.07
80 3 0.77 0.41 0.16
30 4 0.24 0.03 0.00
40 4 0.39 0.08 0.01
60 4 0.58 0.20 0.05
80 4 0.76 0.41 0.17
Desirable regimen (relapse rate = 1.5%)
30 5 0.16 0.01 0.00
40 5 0.23 0.03 0.00
60 5 0.37 0.06 0.01
80 5 0.53 0.16 0.04
All minimal
Relapse rate of 2.5%
P(stopped for futility on the basis of relapse)
nk regimen At least 1 At least 2 At least 3
nk = 30
30 1 0.00 0.00 0.00
30 2 0.57 0.21 0.06
30 3 0.61 0.25 0.07
30 4 0.61 0.23 0.06
30 5 0.70 0.33 0.11
nk = 40
40 1 0.00 0.00 0.00
40 2 0.83 0.52 0.25
40 3 0.82 0.51 0.23
40 4 0.79 0.45 0.19
40 5 0.83 0.51 0.25
nk = 60
60 1 0.00 0.00 0.00
60 2 0.95 0.79 0.56
60 3 0.97 0.84 0.63
60 4 0.95 0.80 0.57
60 5 0.96 0.80 0.56
nk = 80
80 1 0.01 0.00 0.00
80 2 0.99 0.95 0.86
80 3 0.99 0.94 0.85
80 4 0.99 0.96 0.86
80 5 1.00 0.96 0.88
Relapse rate of 5%
P(stopped for futility on the basis of relapse)
nk regimen At least 1 At least 2 At least 3
nk = 30
30 1 0.00 0.00 0.00
30 2 0.84 0.52 0.23
30 3 0.87 0.59 0.30
30 4 0.86 0.57 0.28
30 5 0.91 0.69 0.41
nk = 40
40 1 0.00 0.00 0.00
40 2 0.97 0.86 0.68
40 3 0.97 0.87 0.69
40 4 0.97 0.84 0.62
40 5 0.98 0.88 0.68
nk = 60
60 1 0.01 0.00 0.00
60 2 1.00 0.99 0.95
60 3 1.00 0.99 0.96
60 4 1.00 0.99 0.95
60 5 1.00 0.99 0.95
nk = 80
80 1 0.01 0.00 0.00
80 2 1.00 1.00 1.00
80 3 1.00 1.00 1.00
80 4 1.00 1.00 0.99
80 5 1.00 1.00 1.00
Relapse rate of 1.5%
P(stopped for futility on the basis of relapse)
nk regimen At least 1 At least 2 At least 3
nk = 30
30 1 0.00 0.00 0.00
30 2 0.41 0.08 0.01
30 3 0.44 0.11 0.02
30 4 0.44 0.12 0.02
30 5 0.51 0.15 0.03
nk = 40
40 1 0.00 0.00 0.00
40 2 0.64 0.27 0.07
40 3 0.64 0.27 0.08
40 4 0.61 0.24 0.07
40 5 0.66 0.27 0.09
nk = 60
60 1 0.00 0.00 0.00
60 2 0.81 0.51 0.23
60 3 0.85 0.57 0.29
60 4 0.84 0.54 0.25
60 5 0.83 0.51 0.26
nk = 80
80 1 0.00 0.00 0.00
80 2 0.95 0.79 0.54
80 3 0.94 0.78 0.54
80 4 0.94 0.79 0.56
80 5 0.95 0.80 0.57
All desirable
Relapse rate of 5% (all)
P(stopped for futility on the basis of relapse)
nk regimen At least 1 At least 2 At least 3
nk = 30
30 1 0.00 0.00 0.00
30 2 0.35 0.06 0.01
30 3 0.40 0.08 0.01
30 4 0.37 0.08 0.01
30 5 0.44 0.11 0.02
nk = 40
40 1 0.00 0.00 0.00
40 2 0.58 0.21 0.05
40 3 0.58 0.21 0.05
40 4 0.54 0.19 0.05
40 5 0.57 0.20 0.05
nk = 60
60 1 0.00 0.00 0.00
60 2 0.78 0.43 0.18
60 3 0.79 0.46 0.22
60 4 0.78 0.44 0.20
60 5 0.77 0.43 0.19
nk = 80
80 1 0.00 0.00 0.00
80 2 0.92 0.72 0.45
80 3 0.91 0.68 0.42
80 4 0.90 0.68 0.43
80 5 0.92 0.71 0.44
Relapse rate of 10% (all)
P(stopped for futility on the basis of relapse)
nk regimen At least 1 At least 2 At least 3
nk = 30
30 1 0.00 0.00 0.00
30 2 0.58 0.20 0.05
30 3 0.63 0.25 0.07
30 4 0.61 0.24 0.07
30 5 0.69 0.33 0.11
nk = 40
40 1 0.00 0.00 0.00
40 2 0.84 0.52 0.25
40 3 0.82 0.51 0.24
40 4 0.81 0.47 0.19
40 5 0.84 0.53 0.25
nk = 60
60 1 0.01 0.00 0.00
60 2 0.95 0.80 0.58
60 3 0.96 0.83 0.62
60 4 0.96 0.82 0.57
60 5 0.95 0.80 0.56
nk = 80
80 1 0.01 0.00 0.00
80 2 0.99 0.97 0.88
80 3 0.99 0.95 0.86
80 4 0.99 0.95 0.86
80 5 1.00 0.96 0.88
Relapse rate of 3% (all)
P(stopped for futility on the basis of relapse)
nk regimen At least 1 At least 2 At least 3
nk = 30
30 1 0.00 0.00 0.00
30 2 0.39 0.08 0.01
30 3 0.26 0.03 0.00
30 4 0.24 0.03 0.00
30 5 0.16 0.01 0.00
nk = 40
40 1 0.00 0.00 0.00
40 2 0.65 0.28 0.08
40 3 0.40 0.09 0.01
40 4 0.39 0.08 0.01
40 5 0.23 0.03 0.00
nk = 60
60 1 0.00 0.00 0.00
60 2 0.83 0.52 0.25
60 3 0.61 0.24 0.07
60 4 0.58 0.20 0.05
60 5 0.37 0.06 0.01
nk = 80
80 1 0.00 0.00 0.00
80 2 0.95 0.80 0.56
80 3 0.77 0.41 0.16
80 4 0.76 0.41 0.17
80 5 0.53 0.16 0.04
Figures
Sub-optimal regimen

Minimal regimen

Desirable regimen

Log10(TTP) and Relapse

nk P(confidence < 0.8, >= 1 relapse) P(confidence < 0.8, >= 2 relapse) P(confidence < 0.8, >= 3 relapse)
Even (TTP). Mixed relapse rates.
Control (relapse rate = 5%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
Regimen 1: suboptimal (TTP slope = 10%, relapse rate = 10%)
30 0.21 0.09 0.02
40 0.29 0.20 0.10
60 0.18 0.10 0.06
80 0.17 0.14 0.11
Regimen 2: minimal (TTP slope = 20%, relapse rate = 5%)
30 0.02 0.01 0.00
40 0.02 0.01 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
Regimen 3: minimal (TTP slope = 30%, relapse rate = 5%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
Regimen 4: desirable (TTP slope = 40%, relapse rate = 2.5%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
High (TTP). Mixed relapse rates.
Control (relapse rate = 5%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
Regimen 1: suboptimal (TTP slope = 35%, relapse rate = 10%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
Regimen 2: minimal (TTP slope = 37%, relapse rate = 5%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
Regimen 3: minimal (TTP slope = 39%, relapse rate = 5%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
Regimen 4: desirable (TTP slope = 41%, relapse rate = 2.5%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
High-low (TTP)
Control (relapse rate = 5%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
Regimen 1: suboptimal (TTP slope = -10%, relapse rate = 10%)
30 0.40 0.11 0.03
40 0.74 0.34 0.13
60 0.77 0.46 0.22
80 0.97 0.85 0.60
Regimen 2: minimal (TTP slope = 10%, relapse rate = 5%)
30 0.08 0.01 0.00
40 0.15 0.03 0.01
60 0.08 0.03 0.01
80 0.09 0.04 0.02
Regimen 3: minimal (TTP slope = 35%, relapse rate = 5%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00
Regimen 4: desirable (TTP slope = 40%, relapse rate = 2.5%)
30 0.00 0.00 0.00
40 0.00 0.00 0.00
60 0.00 0.00 0.00
80 0.00 0.00 0.00

Log10(TTP) OR Relapse

Mixed Relapse Rates
Figures

Control Relapse Rate 5%
Probability of stopping a regimen for futility based on the specified thresholds. Note, this assumes the regimens have mixed relapse rates (specified in each row) and that the control regimen has a relapse rate of 5%. The goal is to stop suboptimal regimens frequently and minimal/desirable regimens infrequently.
nk P(confidence < 0.8 OR >= 1 relapse) P(confidence < 0.8 OR >= 2 relapse) P(confidence < 0.8 OR >= 3 relapse)
Even (TTP). Mixed relapse rates.
Control (relapse rate = 5%)
30 1.00 1.00 1.00
40 1.00 1.00 1.00
60 1.00 1.00 1.00
80 1.00 1.00 1.00
Regimen 1: suboptimal (TTP slope = 10%, relapse rate = 10%)
30 0.74 0.48 0.39
40 0.88 0.68 0.50
60 0.99 0.96 0.88
80 1.00 0.99 0.98
Regimen 2: minimal (TTP slope = 20%, relapse rate = 5%)
30 0.43 0.14 0.07
40 0.59 0.22 0.07
60 0.96 0.82 0.55
80 0.98 0.91 0.77
Regimen 3: minimal (TTP slope = 30%, relapse rate = 5%)
30 0.35 0.07 0.01
40 0.54 0.18 0.04
60 0.95 0.81 0.55
80 0.98 0.92 0.78
Regimen 4: desirable (TTP slope = 40%, relapse rate = 2.5%)
30 0.26 0.03 0.00
40 0.35 0.07 0.01
60 0.86 0.48 0.14
80 0.92 0.71 0.43
High (TTP). Mixed relapse rates.
Control (relapse rate = 5%)
30 1.00 1.00 1.00
40 1.00 1.00 1.00
60 1.00 1.00 1.00
80 1.00 1.00 1.00
Regimen 1: suboptimal (TTP slope = 35%, relapse rate = 10%)
30 0.63 0.27 0.07
40 0.90 0.68 0.39
60 0.99 0.95 0.86
80 1.00 0.99 0.97
Regimen 2: minimal (TTP slope = 37%, relapse rate = 5%)
30 0.41 0.09 0.01
40 0.73 0.37 0.12
60 0.95 0.83 0.56
80 0.99 0.92 0.79
Regimen 3: minimal (TTP slope = 39%, relapse rate = 5%)
30 0.43 0.09 0.01
40 0.70 0.33 0.08
60 0.93 0.79 0.54
80 0.98 0.93 0.81
Regimen 4: desirable (TTP slope = 41%, relapse rate = 2.5%)
30 0.25 0.03 0.01
40 0.51 0.12 0.02
60 0.84 0.49 0.13
80 0.92 0.72 0.40
High-low (TTP)
Control (relapse rate = 5%)
30 1.00 1.00 1.00
40 1.00 1.00 1.00
60 1.00 1.00 1.00
80 1.00 1.00 1.00
Regimen 1: suboptimal (TTP slope = -10%, relapse rate = 10%)
30 1.00 0.99 0.99
40 1.00 0.99 0.99
60 1.00 1.00 1.00
80 1.00 1.00 1.00
Regimen 2: minimal (TTP slope = 10%, relapse rate = 5%)
30 0.72 0.46 0.38
40 0.83 0.55 0.40
60 0.96 0.85 0.69
80 0.98 0.92 0.82
Regimen 3: minimal (TTP slope = 35%, relapse rate = 5%)
30 0.53 0.15 0.02
40 0.69 0.29 0.08
60 0.95 0.81 0.58
80 0.98 0.90 0.78
Regimen 4: desirable (TTP slope = 40%, relapse rate = 2.5%)
30 0.42 0.07 0.00
40 0.52 0.14 0.02
60 0.84 0.50 0.16
80 0.93 0.73 0.45
Control Relapse Rate 10%
Probability of stopping a regimen for futility based on the specified thresholds. Note, this assumes the regimens have mixed relapse rates (specified in each row) and that the control regimen has a relapse rate of 10%. The goal is to stop suboptimal regimens frequently and minimal/desirable regimens infrequently.
nk P(confidence < 0.8 OR >= 1 relapse) P(confidence < 0.8 OR >= 2 relapse) P(confidence < 0.8 OR >= 3 relapse)
Even (TTP). Mixed relapse rates.
Control (relapse rate = 10%)
30 1.00 1.00 1.00
60 1.00 1.00 1.00
Regimen 1: suboptimal (TTP slope = 10%, relapse rate = 20%)
30 0.90 0.72 0.52
60 1.00 1.00 0.99
Regimen 2: minimal (TTP slope = 20%, relapse rate = 10%)
30 0.63 0.28 0.12
60 0.99 0.95 0.88
Regimen 3: minimal (TTP slope = 30%, relapse rate = 10%)
30 0.65 0.25 0.06
60 0.99 0.95 0.87
Regimen 4: desirable (TTP slope = 40%, relapse rate = 5%)
30 0.45 0.12 0.02
60 0.94 0.80 0.51
High (TTP). Mixed relapse rates.
Control (relapse rate = 10%)
30 1.00 1.00 1.00
60 1.00 1.00 1.00
Regimen 1: suboptimal (TTP slope = 35%, relapse rate = 20%)
30 0.86 0.59 0.32
60 1.00 1.00 0.99
Regimen 2: minimal (TTP slope = 37%, relapse rate = 10%)
30 0.71 0.34 0.10
60 1.00 0.96 0.88
Regimen 3: minimal (TTP slope = 39%, relapse rate = 10%)
30 0.66 0.30 0.09
60 0.99 0.96 0.89
Regimen 4: desirable (TTP slope = 41%, relapse rate = 5%)
30 0.50 0.12 0.02
60 0.94 0.79 0.50
High-low (TTP)
Control (relapse rate = 10%)
30 1.00 1.00 1.00
60 1.00 1.00 1.00
Regimen 1: suboptimal (TTP slope = -10%, relapse rate = 20%)
30 1.00 1.00 0.99
60 1.00 1.00 1.00
Regimen 2: minimal (TTP slope = 10%, relapse rate = 10%)
30 0.85 0.63 0.45
60 0.99 0.97 0.92
Regimen 3: minimal (TTP slope = 35%, relapse rate = 10%)
30 0.74 0.40 0.12
60 0.99 0.96 0.87
Regimen 4: desirable (TTP slope = 40%, relapse rate = 5%)
30 0.62 0.19 0.02
60 0.95 0.78 0.55
Control Relapse Rate 3%
Probability of stopping a regimen for futility based on the specified thresholds. Note, this assumes the regimens have mixed relapse rates (specified in each row) and that the control regimen has a relapse rate of 3%. The goal is to stop suboptimal regimens frequently and minimal/desirable regimens infrequently.
nk P(confidence < 0.8 OR >= 1 relapse) P(confidence < 0.8 OR >= 2 relapse) P(confidence < 0.8 OR >= 3 relapse)
Even (TTP). Mixed relapse rates.
Control (relapse rate = 3%)
30 1.00 1.00 1.00
60 1.00 1.00 1.00
Regimen 1: suboptimal (TTP slope = 10%, relapse rate = 6%)
30 0.62 0.42 0.37
60 0.98 0.89 0.71
Regimen 2: minimal (TTP slope = 20%, relapse rate = 3%)
30 0.30 0.08 0.06
60 0.88 0.64 0.28
Regimen 3: minimal (TTP slope = 30%, relapse rate = 3%)
30 0.26 0.03 0.00
60 0.87 0.55 0.21
Regimen 4: desirable (TTP slope = 40%, relapse rate = 1.5%)
30 0.16 0.01 0.00
60 0.73 0.24 0.05
High (TTP). Mixed relapse rates.
Control (relapse rate = 3%)
30 1.00 1.00 1.00
60 1.00 1.00 1.00
Regimen 1: suboptimal (TTP slope = 35%, relapse rate = 6%)
30 0.44 0.08 0.01
60 0.95 0.85 0.60
Regimen 2: minimal (TTP slope = 37%, relapse rate = 3%)
30 0.32 0.04 0.00
60 0.87 0.58 0.27
Regimen 3: minimal (TTP slope = 39%, relapse rate = 3%)
30 0.27 0.03 0.00
60 0.87 0.57 0.22
Regimen 4: desirable (TTP slope = 41%, relapse rate = 1.5%)
30 0.20 0.02 0.00
60 0.76 0.27 0.04
High-low (TTP)
Control (relapse rate = 3%)
30 1.00 1.00 1.00
60 1.00 1.00 1.00
Regimen 1: suboptimal (TTP slope = -10%, relapse rate = 6%)
30 1.00 0.99 0.99
60 1.00 1.00 1.00
Regimen 2: minimal (TTP slope = 10%, relapse rate = 3%)
30 0.61 0.41 0.37
60 0.92 0.67 0.40
Regimen 3: minimal (TTP slope = 35%, relapse rate = 3%)
30 0.35 0.05 0.01
60 0.88 0.55 0.23
Regimen 4: desirable (TTP slope = 40%, relapse rate = 1.5%)
30 0.26 0.02 0.00
60 0.75 0.22 0.02
All Desirable Relapse Rates
Control Relapse Rate 3%
Probability of stopping a regimen for futility based on the specified thresholds. Note, this assumes the regimens all have desirable relapse rates (specified in each row) and that the control regimen has a relapse rate of 3%. The goal is to stop suboptimal regimens frequently and minimal/desirable regimens infrequently.
nk P(confidence < 0.8 OR >= 1 relapse) P(confidence < 0.8 OR >= 2 relapse) P(confidence < 0.8 OR >= 3 relapse)
Even (TTP). All desirable relapse rates.
Control (relapse rate = 3%)
30 1.00 1.00 1.00
40 1.00 1.00 1.00
60 1.00 1.00 1.00
80 1.00 1.00 1.00
Regimen 1: (TTP slope = 10%, relapse rate = 1.5%)
30 0.61 0.41 0.37
40 0.77 0.52 0.38
60 0.98 0.89 0.71
80 0.99 0.95 0.88
Regimen 2: (TTP slope = 20%, relapse rate = 1.5%)
30 0.46 0.16 0.08
40 0.66 0.32 0.12
60 0.88 0.64 0.28
80 0.95 0.76 0.48
Regimen 3: (TTP slope = 30%, relapse rate = 1.5%)
30 0.47 0.14 0.03
40 0.62 0.24 0.07
60 0.87 0.55 0.21
80 0.93 0.77 0.50
Regimen 4: (TTP slope = 40%, relapse rate = 1.5%)
30 0.50 0.14 0.03
40 0.67 0.25 0.09
60 0.73 0.24 0.05
80 0.86 0.52 0.19
High (TTP). All desirable relapse rates.
Control (relapse rate = 3%)
30 1.00 1.00 1.00
40 1.00 1.00 1.00
60 1.00 1.00 1.00
80 1.00 1.00 1.00
Regimen 1: (TTP slope = 35%, relapse rate = 1.5%)
30 0.46 0.10 0.01
40 0.78 0.42 0.13
60 0.95 0.85 0.60
80 0.99 0.96 0.86
Regimen 2: (TTP slope = 37%, relapse rate = 1.5%)
30 0.53 0.15 0.02
40 0.79 0.43 0.16
60 0.87 0.58 0.27
80 0.95 0.79 0.51
Regimen 3: (TTP slope = 39%, relapse rate = 1.5%)
30 0.50 0.14 0.03
40 0.75 0.39 0.14
60 0.87 0.57 0.22
80 0.94 0.79 0.54
Regimen 4: (TTP slope = 41%, relapse rate = 1.5%)
30 0.59 0.18 0.04
40 0.80 0.46 0.16
60 0.76 0.27 0.04
80 0.84 0.45 0.14
High-low (TTP). All desirable relapse rates.
Control (relapse rate = 3%)
30 1.00 1.00 1.00
40 1.00 1.00 1.00
60 1.00 1.00 1.00
80 1.00 1.00 1.00
Regimen 1: (TTP slope = -10%, relapse rate = 1.5%)
30 1.00 0.99 0.99
40 1.00 0.99 0.99
60 1.00 1.00 1.00
80 1.00 1.00 1.00
Regimen 2: (TTP slope = 10%, relapse rate = 1.5%)
30 0.73 0.48 0.38
40 0.82 0.59 0.41
60 0.92 0.67 0.40
80 0.95 0.80 0.56
Regimen 3: (TTP slope = 35%, relapse rate = 1.5%)
30 0.58 0.20 0.03
40 0.77 0.39 0.13
60 0.88 0.55 0.23
80 0.94 0.75 0.49
Regimen 4: (TTP slope = 40%, relapse rate = 1.5%)
30 0.67 0.28 0.06
40 0.79 0.43 0.18
60 0.75 0.22 0.02
80 0.84 0.52 0.15
nk P(confidence < 0.8 OR >= 1 relapse) P(confidence < 0.8 OR >= 2 relapse) P(confidence < 0.8 OR >= 3 relapse)
Even (TTP). Mixed relapse rates.
Control (relapse rate = 5%)
30 1.00 1.00 1.00
Regimen 1: desirable (TTP slope = 10%, relapse rate = 2.5%)
30 0.71 0.48 0.39
Regimen 2: desirable (TTP slope = 20%, relapse rate = 2.5%)
30 0.62 0.30 0.12
Regimen 3: desirable (TTP slope = 30%, relapse rate = 2.5%)
30 0.59 0.23 0.04
Regimen 4: desirable (TTP slope = 40%, relapse rate = 2.5%)
30 0.70 0.32 0.12
High (TTP). Mixed relapse rates.
Control (relapse rate = 5%)
30 1.00 1.00 1.00
Regimen 1: desirable (TTP slope = 35%, relapse rate = 2.5%)
30 0.64 0.25 0.07
Regimen 2: desirable (TTP slope = 37%, relapse rate = 2.5%)
30 0.68 0.31 0.10
Regimen 3: desirable (TTP slope = 39%, relapse rate = 2.5%)
30 0.66 0.27 0.07
Regimen 4: desirable (TTP slope = 41%, relapse rate = 2.5%)
30 0.75 0.40 0.13
High-low (TTP)
Control (relapse rate = 5%)
30 1.00 1.00 1.00
Regimen 1: desirable (TTP slope = -10%, relapse rate = 2.5%)
30 1.00 0.99 0.99
Regimen 2: desirable (TTP slope = 10%, relapse rate = 2.5%)
30 0.86 0.62 0.45
Regimen 3: desirable (TTP slope = 35%, relapse rate = 2.5%)
30 0.77 0.38 0.15
Regimen 4: desirable (TTP slope = 40%, relapse rate = 2.5%)
30 0.81 0.49 0.19

Single Analysis

Full data

interim 1
regimen No. patients No. relapses Median FU (weeks) Min FU (weeks) Max FU (weeks) Median percent change in TTP slope CI.l on percent change in TTP slope CI.u on percent change in TTP slope Confidence regimen has steeper slope than control Confidence regimen is best Confidence regimen is one of top two best
1 36 1 20.14 13.29 28.86 0.00 0.00
2 30 1 19.50 13.00 29.86 0.05 -0.08 0.21 0.77 0.00 0.00
3 31 3 22.86 15.86 29.86 0.08 -0.06 0.23 0.87 0.00 0.01
4 31 2 20.86 13.29 29.86 0.29 0.13 0.47 1.00 0.24 0.99
5 34 1 21.86 13.00 30.00 0.35 0.19 0.53 1.00 0.76 1.00
interim 2
regimen No. patients No. relapses Median FU (weeks) Min FU (weeks) Max FU (weeks) Median percent change in TTP slope CI.l on percent change in TTP slope CI.u on percent change in TTP slope Confidence regimen has steeper slope than control Confidence regimen is best Confidence regimen is one of top two best
1 60 1 28.36 13.00 41.43 0.00 0
2 60 2 25.36 13.14 42.43 0.09 -0.01 0.22 0.96 0.00 0
3 60 4 28.86 13.43 42.43 0.16 0.06 0.29 1.00 0.00 0
4 60 3 26.07 13.14 42.43 0.33 0.21 0.48 1.00 0.14 1
5 60 1 28.21 13.43 42.57 0.40 0.28 0.55 1.00 0.86 1 
## [1] 81.85714

Interim 1

Number of relapses observed per regimen by the first interim analysis.
regimen No. relapses
1 1
2 1
3 3
4 2
5 1
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.850 0.015 0.821 0.879 1.001 3361.627 3334.667
week 0.087 0.005 0.078 0.096 1.001 2973.382 3317.836
week:regimen2 0.005 0.006 -0.007 0.017 1.000 3119.470 2969.695
week:regimen3 0.007 0.006 -0.005 0.019 1.000 2882.399 3290.040
week:regimen4 0.025 0.007 0.012 0.038 1.001 3024.336 3016.201
week:regimen5 0.030 0.007 0.017 0.043 1.001 2788.192 3243.151

How confident are we that regimen 4 is better than all other regimens?

regimen prop_best bestarm
1 0.0000 regimen1
2 0.0000 regimen2
3 0.0000 regimen3
4 0.2377 regimen4
5 0.7622 regimen5

How confident are we that our chosen subset contains the best regimen?

##   perc.confidence subset.size
## 1         0.85800           1
## 2         0.99975           2
## 3         1.00000           3
## 4         1.00000           4

How certain can we be that the rate of change in log10(TTP) for any regimen is different from the rate of change for the control?

Interim 2

Final Analysis

Timelines

R Version

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          1.2                         
## year           2021                        
## month          11                          
## day            01                          
## svn rev        81115                       
## language       R                           
## version.string R version 4.1.2 (2021-11-01)
## nickname       Bird Hippie